Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1214 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1214 conjugacy classes of subgroups — too many to draw. Only its 191 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #22598736 | C2 | semidirect |
| 3. #22589569 | C2 | semidirect |
| 4. #22589258 | C2 | semidirect |
| 5. #22588298 | C2 | semidirect |
| 6. C4×#14556047 | C2 | semidirect |
| 7. C71×#2568 | C2 | semidirect |
| 188. #2568 | D71 | semidirect |
| 193. C71 | #25872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22602111 | 2 |
| #22598736 | 2 |
| #22589569 | 2 |
| #22589258 | 2 |
| #22588298 | 2 |
| C4×#14556047 | 2 |
| C71×#2568 | 2 |
| #25872 | 71 |